Quantum theory has attracted people's attention since it was proposed. Due to its unique advantages in information storage and processing, quantum information processing has become the most popular research field. Quantum theory also provides us with new methods or concepts for information manipulation and processing. The basic problems of classical physics are basically trying to be solved in a situation of isolation from the surrounding environment to reduce the complexity of the analysis problem, but the quantum system inevitably produces decoherence and establishes a close relationship with the environment such as entanglement, so the formal framework of quantum mechanics is inherently capable of depicting complex relationships. Based on the principle of quantum open system, a classifier under the formal framework of quantum mechanics is established to simulate the evolution process of open systems, that is, the interaction process between the target system and the environment. Specifically, we regard the features (or attributes) of the sample as environmental factors that affect the decision-making of the target system, and the target system can obtain the categories (or labels) of the sample through measurement. Based on this, we use the formal framework of quantum mechanics to establish a more natural and tighter correspondence between attributes and labels. Limited by the limitations of simulating quantum operations on classical computers, we conducted experiments on two lightweight machine learning datasets and compared them with mainstream classification algorithms. Experimental results show that the classification algorithm is better than the comparison models, and it also reveals the potential of the algorithm.
Quantum theory has attracted people's attention since it was proposed. Due to its unique advantages in information storage and processing, quantum information processing has become the most popular research field. Quantum theory also provides us with new methods or concepts for information manipulation and processing. The basic problems of classical physics are basically trying to be solved in a situation of isolation from the surrounding environment to reduce the complexity of the analysis problem, but the quantum system inevitably produces decoherence and establishes a close relationship with the environment such as entanglement, so the formal framework of quantum mechanics is inherently capable of depicting complex relationships. Based on the principle of quantum open system, a classifier under the formal framework of quantum mechanics is established to simulate the evolution process of open systems, that is, the interaction process between the target system and the environment. Specifically, we regard the features (or attributes) of the sample as environmental factors that affect the decision-making of the target system, and the target system can obtain the categories (or labels) of the sample through measurement. Based on this, we use the formal framework of quantum mechanics to establish a more natural and tighter correspondence between attributes and labels. Limited by the limitations of simulating quantum operations on classical computers, we conducted experiments on two lightweight machine learning datasets and compared them with mainstream classification algorithms. Experimental results show that the classification algorithm is better than the comparison models, and it also reveals the potential of the algorithm.
In machine learning, classification algorithms often use statistical methods to build the correspondence between features (or attributes) and categories (or labels), that is, the statistical correlation between features and categories. In quantum theory, a large number of experimental results show that quantum correlation is far stronger than what can be explained by local hidden theory (i.e., classical or non-quantum theory), that is, quantum mechanics theory reveals a statistical correlation stronger than that described by classical theory. Based on this, this paper will use the strong statistical correlation revealed by Bell state to build a classification algorithm to verify the validity and superiority of the formal framework of quantum mechanics in specific classification tasks. Specifically, we use quantum joint probabilities derived from the measurement process of Bell state to model the quantum statistical correlation between features and categories. The paper first theoretically proves that the formal framework used has the ability to violate Bell inequality; moreover, a classification algorithm is implemented and verified on classic machine learning datasets. Experimental results show that the algorithm is significantly better than most mainstream machine learning algorithms.
Machine Learning classification models learn the relation between input as features and output as a class in order to predict the class for the new given input. Several research works have demonstrated the effectiveness of machine learning algorithms but the state-of-the-art algorithms are based on the classical theories of probability and logic. Quantum Mechanics (QM) has already shown its effectiveness in many fields and researchers have proposed several interesting results which cannot be obtained through classical theory. In recent years, researchers have been trying to investigate whether the QM can help to improve the classical machine learning algorithms. It is believed that the theory of QM may also inspire an effective algorithm if it is implemented properly. From this inspiration, we propose the quantum-inspired binary classifier, which is based on quantum detection theory. We used text corpora and image corpora to explore the effect of our proposed model. Our proposed model outperforms the state-of-the-art models in terms of precision, recall, and F-measure for several topics (categories) in the 20 newsgroup text corpora. Our proposed model outperformed all the baselines in terms of recall when the MNIST handwritten image dataset was used; F-measure is also higher for most of the categories and precision is also higher for some categories. Our proposed model suggests that binary classification effectiveness can be achieved by using quantum detection theory. In particular, we found that our Quantum-Inspired Binary Classifier can increase the precision, recall, and F-measure of classification where the state-of-the-art methods cannot.
Machine Learning classification models learn the relation between input as features and output as a class in order to predict the class for the new given input. Quantum Mechanics (QM) has already shown its effectiveness in many fields and researchers have proposed several interesting results which cannot be obtained through classical theory. In recent years, researchers have been trying to investigate whether the QM can help to improve the classical machine learning algorithms. It is believed that the theory of QM may also inspire an effective algorithm if it is implemented properly. From this inspiration, we propose the quantum-inspired binary classifier.
This paper investigates the potential of combining quantum machine learning with quantum feature selection to enhance the performance of machine learning models. The core idea is to frame the machine learning problem as a quantum feature selection problem, leveraging quantum phenomena such as entanglement and superposition to effectively identify the most informative features. Traditional feature selection methods often struggle with high-dimensional datasets and may not fully exploit the inherent correlations between features. Quantum feature selection, utilizing quantum computers, offers a fundamentally different approach, potentially capable of identifying subtle relationships and patterns that classical methods miss. This paper explores the theoretical framework, outlining the conversion process and the utilization of quantum mechanics to optimize feature selection. The proposed method aims to achieve superior classification and regression results compared to conventional machine learning algorithms. We present a detailed mathematical description of the process, emphasizing the key quantum concepts involved. The ultimate goal is to demonstrate a viable pathway for advancing machine learning capabilities through the integration of quantum computing principles.
Due to the similarity of the computational and probabilistic nature of quantum computing and machine learning, the idea arose to optimize the learning process using quantum methods. There are both fundamentally new algorithms, such as HHL, and quantum-improved ones: QPCA, QSVM. In this article, we will look at the QSVM algorithm step by step, starting from the basics described in section 2 and gradually delving into the composition of the algorithm. Thus, after the basics, we will consider the quantum phase estimation, which is part of the HHL algorithm, and then the QSVM algorithm, the component of which is the HHL. We also will consider the QPCA algorithm, which can be applied before the QSVM algorithm to reduce the dimension of the data sample. In this way, we explore the fundamental difference between classical algorithms and their quantum counterparts. We also implement the QSVM method in practice and compare the obtained practical results with theory. As a result, we obtained high quality of accuracy (100 %) compared to the classical SVM (83 %) on a data sample of dimension 72. However, we found out that the learning time on a quantum device is far from ideal (it can reach 5 min for a sample of this size). The study aims to theoretically argue or disprove the hypothesis about the efficiency of quantum computing for machine learning algorithms. The object of research is the programming of quantum computers. The research subject is the study of quantum computing mechanisms for the implementation of machine learning problems. The research result is a software module that allows evaluating the efficiency of the classification task on a quantum computer. It also can be used to compare the results obtained from classical and quantum devices. Research methods: theoretical analysis of the foundations of quantum computing: principles of superposition and entanglement, linear algebra, probability theory over complex numbers; building a model of one qubit and multi-qubit system; research of quantum machine learning algorithms’ work principles and their complexity; empirical comparison of quantum machine learning methods with their classical counterparts.
Quantum mechanics, a fundamental theory in physics that describes the behavior of nature at atomic and subatomic scales, offers significant advantages over classical physics in various contexts. These advances have laid the foundation for the field of quantum computing, which leverages the unique properties of quantum mechanics to solve complex computational problems more efficiently than classical computers. At the core of quantum computing are qubits, the quantum analogs of classical bits. Unlike classical bits, which are restricted to binary states (0 or 1), qubits utilize superposition and entanglement, enabling them to exist in multiple states simultaneously and interact in ways that amplify computational capabilities. This study presents an overview of quantum algorithms and tools for quantum machine learning, with a focus on recent advancements. Through a comparative analysis and empirical evidence, the research highlights the potential advantages of quantum algorithms in various applications, such as data processing, pattern recognition, and algorithmic complexity. The findings suggest that quantum methods may surpass their classical counterparts in certain domains. However, a key challenge remains: the current limitations of quantum hardware. Despite the theoretical benefits, practical implementation is constrained by the noisy and error-prone nature of quantum devices. Consequently, the experiments conducted in this study were performed in simulation environments, which demonstrated potential improvements when applying quantum paradigms.